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Study of discrete-time Hawkes process and its compensator

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  • Sarma, Utpal Jyoti Deba
  • Selvamuthu, Dharmaraja

Abstract

The discrete-time Hawkes process (DTHP) is a sub-class of g-functions that serves as a discrete-time version of the continuous-time Hawkes process (CTHP). Like the CTHP, the DTHP also has the self-exciting property and its intensity depends on the entire history. In this paper, we study the asymptotic behavior of the DTHP and its compensator. We further analyze the moment generating function (MGF) of the DTHP and obtain some bounds and convergence results on the scaled logarithmic MGF of the DTHP.

Suggested Citation

  • Sarma, Utpal Jyoti Deba & Selvamuthu, Dharmaraja, 2024. "Study of discrete-time Hawkes process and its compensator," Statistics & Probability Letters, Elsevier, vol. 214(C).
    • Handle: RePEc:eee:stapro:v:214:y:2024:i:c:s0167715224001615
    DOI: 10.1016/j.spl.2024.110192
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